Under compression loading, bulk metallic glasses (BMGs) irreversibly deform through shear banding manifested as a serrated flow behavior. By using a statistical analysis together with a complementary dynamical analysis of the stress-time curves during serrated flow, we characterize the distinct spatiotemporal dynamical regimes and find that the plastic dynamic behavior of a Cu50Zr45Ti5 BMG changes from chaotic to self-organized critical behavior with increasing strain rate. This plastic dynamics transition with the strain rate is interpreted in the frame of the competence between the neighboring elastic strain field forming and relaxation processes.